1. Technical Field of the Invention
The present invention relates to a technology for synthesizing a musical tone signal by performing a simulation according to a predetermined physical model on the basis of a sounding mechanism of a natural musical instrument. Particularly, the invention relates to a musical tone signal synthesis method, a program and a musical tone signal synthesis apparatus suitable to generate a musical tone signal that realistically expresses characteristics of a sound generated from a musical instrument having a three-dimensional structure having a string and a main body (a component that supports the string and emits a sound to the air).
2. Description of the Related Art
There is known a method for synthesizing a musical tone of a natural musical instrument in a pseudo or virtual manner according to a predetermined physical model based on a sounding mechanism of the natural musical instrument in a dedicated hardware system including a general purpose computer, a digital signal processing apparatus such as a digital signal processor (DSP), an integrated circuit, a large-scale integrated circuit, etc. When a pseudo piano sound needs to be generated, for example, a musical tone signal is synthesized by executing a simulating operation in a general purpose computer on the basis of a string physical model. For instance, there is a musical tone signal synthesis apparatus that synthesizes a musical tone signal based on a cyclic signal generated by inputting an excitation signal to a closed loop using a delay element. This musical tone signal synthesis apparatus is described in Patent Reference 1 and Patent Reference 2, for example.    [Patent Reference 1] Japanese Patent Publication No. 2820205    [Patent Reference 2] Japanese Patent Publication No. 2591198
One end of a piano string is supported by a bearing on a frame corresponding to a part of the main body of a piano, and the other end thereof is supported by a bridge on a sound board corresponding to a part of the main body. When a key is pressed, a string corresponding to the key is released from a damper and, simultaneously, kinetic energy is applied to a hammer. When the hammer strikes the string, some of energy of wave excited in the string is transmitted to the main body via the string supports and the remainder is reflected at the string supports to remain in the string. The wave generated in the string repeatedly reciprocates between the string supports to generate vibration. While vibration in a direction perpendicular to the axial direction of the string, that is, bending vibration is initially generated in a direction in which the string is stroke by the hammer, vibration is generated even in a direction perpendicular to the direction in which the string is stroke by the hammer due to the influence of the bridge which moves three-dimensionally. The string generates vibration in the axial direction of the string, that is, longitudinal vibration, in addition to the bending vibrations in the two directions.
The piano generates a full stereoscopic characteristic musical tone by vibrating not only the string but also the main body having a complicated three-dimensional shape including a sound board, a frame, a pillar, a side board, a deck, etc.
However, there has not been proposed a method (calculation algorithm) for realistically expressing characteristics of a musical tone generated from the piano that is a structure having a string corresponding to a part for generating a musical scale, and a main body corresponding to a part for supporting the string and emitting a sound to the air.